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Chord progression inversion notation

Greetings.

It seems that in Theory Tab, there are 1st and 2nd chord inversions shown on the piano keys, but not on the corresponding chord notations. This is leading to confusion.

In addition, the bass note is always correct for the chord, but, at times, there is an absence of the root in the chord itself. Ex) a min is shown on the piano with A as the base, then E , C, and E.

I am a music theory novice.
Thank you for addressing my concerns.

Paul